Question

If f(x)= 2x sin(x) cos(x), how do you find f'(x)?

Answer 1

Alternative answer:

Use trigonometry (sine of 2x) to rewrite the function first:

`f(x)=2xsinxcosx=x(2sinxcosx)=xsin(2x)`

Now use the product rule and use the chain rule to get:

`f'(x)=(1)(sin(2x)) + (x)(cos(2x)*2)`

Simpply to get:

`f'(x) = sin(2x)+2xcos(2x)`

I know it doesn't look the same as the other answer. Use trigonometric identities to see that the answers are equivalent.